Solve (5/8)^6X7^3=

$$( \frac { 5 } { 8 } ) ^ { 6 } X 7 ^ { 3 } =$$

Evaluate

$$\frac{5359375X}{262144}$$

Solution Steps

Calculate \frac{5}{8} to the power of 6 and get \frac{15625}{262144}.

$$\frac{15625}{262144}X\times 7^{3}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{15625}{262144}X\times 343$$

Express \frac{15625}{262144}\times 343 as a single fraction.

$$\frac{15625\times 343}{262144}X$$

Multiply 15625 and 343 to get 5359375.

$$\frac{5359375}{262144}X$$

Differentiate w.r.t. X

$$\frac{5359375}{262144} = 20\frac{116495}{262144} = 20.444393157958984$$

Steps Using Definition of a Derivative

Calculate \frac{5}{8} to the power of 6 and get \frac{15625}{262144}.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{15625}{262144}X\times 7^{3})$$

Calculate 7 to the power of 3 and get 343.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{15625}{262144}X\times 343)$$

Express \frac{15625}{262144}\times 343 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{15625\times 343}{262144}X)$$

Multiply 15625 and 343 to get 5359375.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{5359375}{262144}X)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{5359375}{262144}X^{1-1}$$

Subtract 1 from 1.

$$\frac{5359375}{262144}X^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{5359375}{262144}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{5359375}{262144}$$